Minimal Irreversible Quantum Mechanics: Decoherence and Classical Equilibrium Limit

Using the Minimal Irreversible Quantum Mechanicsformalism, it is demonstrated that the quantum regimecan be considered as the transient phase while the finalclassical equilibrium regime is the permanent state. A basis where exact matrix decoherenceappears for these final states is found. The appearanceof a classical universe in quantum gravity models is thecosmological version of this problem.